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Answer 1 · 2017-11-13T12:35:40

# 8# th term of the sequence is #-128x^8 -384x^7 #

Geometric sequence :

#a_1= (x+3) , a_2= (-2x^2-6x) = -2x(x+3)= -2x*a_1#

# a_3= 4x^3+12x^2 = -2x(-2x^2-6x) = -2x* a_2#

First term is #a_1= (x+3)# and common ratio is # r= -2x#

#n# th term of G.P is # a_n= a_1*r^(n-1)#

#:. 8# th term of the sequence is # a_8= a_1*(-2x)^(8-1)# or

# a_8= (x+3)*(-2x)^(8-1) or a_8= (x+3)*(-2x)^7 # or

# a_8= (x+3)*(-128x^7) or a_8= -128x^7(x+3) # or

#a_8= -128x^8 -384x^7 #

#:. 8# th term of the sequence is #-128x^8 -384x^7 # [Ans]